1. In human engineering and product design, it is often important to consider the weights of people, so that airplanes or elevators do not get overloaded, chairs do not break, etc. According to data from the National Health Survey, the weights of men in the United States are normally distributed with a mean of 173 pounds and a standard deviation of 30 pounds. Answer the following questions, giving careful reasons for your answers. Use Excel or the standard normal tables; the box at the end of this assignment describes Excel's NORM.DIST functions. (a) One man is randomly selected from the U.S. population. What is the probability that he weighs more than 180 pounds? Explain your answer. (b) 36 men are randomly selected from the U.S. population. What is the probability that the average weight of these 36 men is greater than 180 pounds? Explain your answer. (c) On the same set of axes, make a rough sketch of the graphs of the probability density functions that you used to find your answers to Questions la and 1b. Discuss the similarities and differences (in shape, centre, spread, etc.) between the two graphs that you have drawn. (d) Use your sketch from Question Ic to explain why your answers to Questions la and 1b are different. Which of the two answers is larger? Is that what you expected? Why, or why not? (e) Suppose 36 men are selected from the same family in the U.S., and you want to know the probability that their average weight is greater than 180 pounds. Could you use the same method to find this probability that you used in Question 1b? Why, or why not